Crystalline assemblies and densest packings of a family of truncated tetrahedra and the role of directional entropic forces

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usa-input-error-message selection-validation-message"> Name must be less than 100 characters </div> </div> <div class="action-panel-control-wrap existing-collections-controls"> <label for="collections-action-panel-add-to-existing" class="action-panel-label"> Choose a collection: </label> <select id="collections-action-panel-add-to-existing" class="action-panel-selector collections-action-add-to-existing" data-ga-category="save_share" data-ga-action="select_collection" data-ga-label="($('#collections-action-add-to-existing').val() === 'Favorites') ? 'Favorites' : 'non_favorites_collection'"> </select> <div class="collections-retry-load-on-error usa-input-error-message selection-validation-message"> Unable to load your collection due to an error<br> <a href="#">Please try again</a> </div> </div> </div> <div class="action-panel-actions"> <button class="action-panel-submit" type="submit" data-loading-label="Adding..." data-pinger-ignore data-ga-category="save_share" data-ga-action="collections" data-ga-label="add"> Add </button> <button class="action-panel-cancel" aria-label="Close 'Add to Collections' panel" ref="linksrc=close_collections_panel" aria-controls="collections-action-panel" aria-expanded="false" data-ga-category="save_share" data-ga-action="collections" data-ga-label="cancel"> Cancel </button> </div> </form> </div> </div> <div id="bibliography-action-panel" class="bibliography-action-panel action-panel in-progress-dots-panel" aria-hidden="true" data-bibliography-open-panel-enabled="false" data-bibliography-open-panel-url-hash="#open-bibliography-panel"> <div class="inner-wrap"> <h3 class="action-panel-heading"> Add to My Bibliography </h3> <form id="bibliography-action-panel-form" class="bibliography-action-panel-form action-panel-content action-form action-panel-smaller-selectors" data-add-to-bibliography-max-amount="100" data-add-to-bibliography-batch-size="10" data-bibliography-delegates-url="/list-bibliography-delegates/" data-add-to-bibliography-url="/add-to-bibliography/" data-get-article-ids-by-search-url="/get-article-ids-by-search/" data-mybib-root-url="https://www.ncbi.nlm.nih.gov/myncbi/collections/mybibliography/"> <input type="hidden" name="csrfmiddlewaretoken" value="bTZTGujsLoIIYYxcSaWiLTqHXPblVatDjMUCz9Vud3saW1S8aR4vsb5eJ098Ukc7"> <div class="action-panel-control-wrap bibliographies-controls"> <div class="choice-group"> <ul class="bibliographies-action-add radio-group-items"> <li> <input name="bibliography" id="my-bibliography" class="my-bibliography" type="radio" checked/> <label for="my-bibliography">My Bibliography</label> </li> </ul> </div> </div> <div class="bibliographies-retry-load-on-error usa-input-error-message selection-validation-message"> Unable to load your delegates due to an error<br> <a href="#">Please try again</a> </div> <div class="action-panel-actions"> <button class="action-panel-submit" type="submit" data-loading-label="Adding..." data-pinger-ignore> Add </button> <button class="action-panel-cancel" aria-label="Close 'Add to bibliography' panel" ref="linksrc=close_bibliography_panel" aria-controls="bibliography-action-panel" aria-expanded="false" data-ga-category="save_share" data-ga-action="mybib" data-ga-label="cancel"> Cancel </button> </div> </form> </div> </div> <div id="saved-search-action-panel" class="saved-search-action-panel action-panel " aria-hidden="true" data-saved-search-open-panel-enabled="false" data-saved-search-open-panel-url-hash="#open-saved-search-panel"> <div class="inner-wrap"> <h2 class="action-panel-heading"> Your saved search </h2> <form id="saved-search-action-panel-form" class="saved-search-action-panel-form action-panel-content action-form" data-create-saved-search-url="/create-saved-search/" data-try-search-terms-url="/try-search-term/" data-saved-search-root-url="https://www.ncbi.nlm.nih.gov/myncbi/searches/"> <input type="hidden" name="csrfmiddlewaretoken" value="bTZTGujsLoIIYYxcSaWiLTqHXPblVatDjMUCz9Vud3saW1S8aR4vsb5eJ098Ukc7"> <div class="action-panel-control-wrap"> <label for="saved-search-name" class="action-panel-label saved-search-name-label required-field-asterisk"> Name of saved search: </label> <input maxlength="200" type="text" name="saved-search-name" id="saved-search-name" class="saved-search-name" value="" required pattern="[^"&=<>\/]*" title="The following characters are not allowed in the Name field: "&=<>/"> </div> <div class="action-panel-control-wrap"> <label for="saved-search-term" class="action-panel-label required-field-asterisk"> Search terms: </label> <textarea name="saved-search-term" id="saved-search-term" class="saved-search-term" required></textarea> </div> <div class="test-search-term-wrap"> <a href="#" class="try-search-term">Test search terms</a> </div> <div class="choice-group action-panel-extra-margin-top"> <span class="action-panel-label" id="fieldset-label"> Would you like email updates of new search results? </span> <fieldset id="saved-search-alert" aria-describedby="fieldset-label"> <legend class="usa-sr-only">Saved Search Alert Radio Buttons</legend> <ul class="radio-group-items"> <li> <input type="radio" id="saved-search-alert-yes" class="saved-search-alert-yes" name="saved-search-alert" value="yes" checked> <label for="saved-search-alert-yes" class="action-panel-label">Yes</label> </li> <li> <input aria-label="No radio input" type="radio" id="saved-search-alert-no" class="saved-search-alert-no" name="saved-search-alert" value="no"> <label for="saved-search-alert-no" class="action-panel-label">No</label> </li> </ul> </fieldset> </div> <div class="alert-schedule-wrap"> <div class="action-panel-control-wrap"> <label class="action-panel-label"> Email: </label> <span aria-label="Email address" id="saved-search-email" class="action-panel-label"><span class="action-panel-label-bold"></span> (<a class="myncbi-account-settings" href="https://www.ncbi.nlm.nih.gov/account/settings/">change</a>)</span> </div> <div class="action-panel-control-wrap action-panel-extra-margin-top"> <label for="saved-search-frequency" class="action-panel-label"> Frequency: </label> <select id="saved-search-frequency" class="no-border-panel-selector saved-search-frequency"> <option value="monthly">Monthly</option> <option value="weekly">Weekly</option> <option value="daily">Daily</option> </select> </div> <div class="action-panel-control-wrap saved-search-monthly-additional"> <label for="saved-search-monthly-on-day" class="action-panel-label"> Which day? </label> <select id="saved-search-monthly-on-day" class="no-border-panel-selector"> <option value="Sunday">The first Sunday</option> <option value="Monday">The first Monday</option> <option value="Tuesday">The first Tuesday</option> <option value="Wednesday">The first Wednesday</option> <option value="Thursday">The first Thursday</option> <option value="Friday">The first Friday</option> <option value="Saturday">The first Saturday</option> <option value="day">The first day</option> <option value="weekday">The first weekday</option> </select> </div> <div class="action-panel-control-wrap saved-search-weekly-additional"> <label for="saved-search-weekly-on-day" class="action-panel-label"> Which day? </label> <select id="saved-search-weekly-on-day" class="no-border-panel-selector saved-search-weekly-on-day"> <option value="Sunday">Sunday</option> <option value="Monday">Monday</option> <option value="Tuesday">Tuesday</option> <option value="Wednesday">Wednesday</option> <option value="Thursday">Thursday</option> <option value="Friday">Friday</option> <option value="Saturday">Saturday</option> </select> </div> <div class="action-panel-control-wrap"> <label for="saved-search-report" class="action-panel-label"> Report format: </label> <select id="saved-search-report" class="no-border-panel-selector saved-search-report"> <option value="DocSum">Summary</option> <option value="DocSumText">Summary (text)</option> <option value="Abstract">Abstract</option> <option value="AbstractText">Abstract (text)</option> <option value="MEDLINE">PubMed</option> </select> </div> <div class="action-panel-control-wrap"> <label for="saved-search-amount" class="action-panel-label"> Send at most: </label> <select id="saved-search-amount" class="no-border-panel-selector saved-search-amount"> <option value="1">1 item</option> <option value="5" selected>5 items</option> <option value="10">10 items</option> <option value="20">20 items</option> <option value="50">50 items</option> <option value="100">100 items</option> <option value="200">200 items</option> </select> </div> <div> <input type="checkbox" id="saved-search-send-if-no-result" class="saved-search-send-if-no-result" name="saved-search-send-if-no-result"> <label for="saved-search-send-if-no-result" class="action-panel-label smaller-checkbox"> Send even when there aren't any new results </label> </div> <div class="action-panel-control-wrap option-text-in-email-wrap"> <label for="saved-search-email-text" class="action-panel-label"> Optional text in email: </label> <textarea name="saved-search-email-text" id="saved-search-email-text" class="saved-search-email-text"></textarea> </div> </div> <div class="action-panel-actions"> <button class="action-panel-submit" type="submit" data-loading-label="Saving..." data-ga-category="save_share" data-ga-action="alert" data-ga-label="save"> Save </button> <button class="action-panel-cancel" aria-label="Close 'Your saved search' panel" ref="linksrc=close_saved_search_panel" aria-controls="saved-search-action-panel" aria-expanded="false" data-ga-category="save_share" data-ga-action="alert" data-ga-label="cancel"> Cancel </button> </div> </form> </div> </div> <div id="citation-manager-action-panel" class="citation-manager-action-panel action-panel" aria-hidden="true"> <div class="inner-wrap"> <h2 class="action-panel-heading"> Create a file for external citation management software </h2> <form id="citation-manager-action-panel-form" class="action-panel-content action-form" action="/results-export-ids/" data-by-search-action="/results-export-search-data/" data-by-ids-action="/results-export-ids/" method="post" data-by-search-method="post" data-by-ids-method="post"> <input type="hidden" name="csrfmiddlewaretoken" value="bTZTGujsLoIIYYxcSaWiLTqHXPblVatDjMUCz9Vud3saW1S8aR4vsb5eJ098Ukc7"> <input name="results-format" type="hidden" value="pubmed"/> <div class="action-panel-actions"> <button class="action-panel-submit" type="submit" data-loading-label="Sending..." data-ga-category="save_share" data-ga-action="citation_manager" data-ga-label="save"> Create file </button> <button class="action-panel-cancel" aria-label="Close 'Send citations to citation manager' panel" ref="linksrc=close_citation_manager_panel" aria-controls="citation-manager-action-panel" aria-expanded="false" data-ga-category="save_share" data-ga-action="citation_manager" data-ga-label="cancel"> Cancel </button> </div> </form> </div> </div> <div id="rss-action-panel" class="rss-action-panel action-panel " aria-hidden="true"> <div class="inner-wrap"> <h2 class="action-panel-heading"> Your RSS Feed </h2> <form id="rss-action-panel-form" class="rss-action-panel-form action-panel-content action-form" data-create-rss-feed-url="/create-rss-feed-url/" data-search-form-term-value=""> <input type="hidden" name="csrfmiddlewaretoken" value="bTZTGujsLoIIYYxcSaWiLTqHXPblVatDjMUCz9Vud3saW1S8aR4vsb5eJ098Ukc7"> <div class="action-panel-control-wrap"> <label for="rss-name" class="action-panel-label required-field-asterisk"> Name of RSS Feed: </label> <input maxlength="200" placeholder="Name" type="text" name="rss-name" id="rss-name" class="rss-name" value='' required pattern="[^"&=<>\/]*" title="The following characters are not allowed in the Name field: "&=<>/"> </div> <div class="rss-limit-wrap"> <div class="action-panel-control-wrap action-panel-extra-margin-top"> <label for="rss-limit" class="action-panel-label"> Number of items displayed: </label> <select id="rss-limit" class="no-border-panel-selector rss-limit"> <option value="5">5</option> <option value="10">10</option> <option value="15" selected="selected">15</option> <option value="20">20</option> <option value="50">50</option> <option value="100">100</option> </select> </div> </div> <div class="action-panel-actions"> <button class="action-panel-submit" type="submit" data-loading-label="Creating..." data-ga-category="save_share" data-ga-action="alert" data-ga-label="save"> Create RSS </button> <button class="action-panel-cancel" aria-label="Close 'Your RSS' panel" ref="linksrc=close_rss_panel" aria-controls="rss-action-panel" aria-expanded="false" data-ga-category="save_share" data-ga-action="alert" data-ga-label="cancel"> Cancel </button> </div> <div class="action-panel-control-wrap rss-link-copy-wrap"> <label for="rss-link" class="usa-sr-only">RSS Link</label> <input placeholder="Your RSS Feed Link" type="text" name="rss-link" id="rss-link" class="rss-link" title="RSS Link"> <button type="button" disabled class="rss-link-copy-button disabled" data-ga-category="save_share" data-ga-action="rss" data-ga-label="copy"> Copy </button> </div> </form> </div> </div> </div> </div> <div class="article-page" id="article-page" data-article-pmid="22098586"> <aside class="page-sidebar"> <div class="inner-wrap"> <div class="full-text-links"> <div class="full-view"> <h3 class="title"> Full text links </h3> <div class="full-text-links-list"> <a class="link-item dialog-focus" href="https://doi.org/10.1021/nn204012y" target="_blank" rel="noopener" ref="linksrc=fulltextorjournal_fulltext&is_pmc=False&PrId=3001&itool=Abstract-def&log$=linkouticon&uid=22098586&db=pubmed&nlmid=101313589" title="See full text options at American Chemical Society" data-ga-category="full_text" data-ga-action="American Chemical Society" data-ga-label="22098586" ><img src="https://cdn.ncbi.nlm.nih.gov/corehtml/query/egifs/http:--pubs.acs.org-images-pubmed-acspubs.jpg" alt="American Chemical Society full text link"><span class="text"> American Chemical Society </span></a> </div> </div> <div class="short-view"> <a href="#" class="full-text-links-button full-text-links-dialog-trigger"> Full text links </a> </div> </div> <div class="actions-buttons sidebar"><h3 class="title">Actions</h3><div class="inner-wrap"><button class="citation-button citation-dialog-trigger" aria-label="Open dialog with citation text in different styles" data-ga-category="save_share" data-ga-action="cite" data-ga-label="open" data-all-citations-url="/22098586/citations/" data-citation-style="nlm" data-pubmed-format-link="/22098586/export/"><span class="button-label">Cite</span></button><link type="text/css" href="ncbi-overlay-block/src/overlay-block.css"><div class="collections-button-container" data-article-id="22098586" data-article-db="pubmed"><button class="collections-button collections-dialog-trigger" aria-label="Save article in MyNCBI collections." data-ga-category="collections_button" data-ga-action="click" data-ga-label="collections_button" data-collections-open-dialog-enabled="false" data-collections-open-dialog-url="https://account.ncbi.nlm.nih.gov/?back_url=https%3A%2F%2Fpubmed.ncbi.nlm.nih.gov%2F22098586%2F%23open-collections-dialog" data-in-collections="false"><span class="button-label">Collections</span></button><div class="overlay" role="dialog"><div id="collections-action-dialog" class="dialog collections-dialog" aria-hidden="true"><div class="title">Add to Collections</div><div class="collections-action-panel action-panel"><form id="collections-action-dialog-form" class="collections-action-panel-form action-panel-content action-form action-panel-smaller-selectors" data-existing-collections-url="/list-existing-collections/" data-add-to-existing-collection-url="/add-to-existing-collection/" data-create-and-add-to-new-collection-url="/create-and-add-to-new-collection/" data-myncbi-max-collection-name-length="100" data-collections-root-url="https://www.ncbi.nlm.nih.gov/myncbi/collections/"><input type="hidden" name="csrfmiddlewaretoken" value="bTZTGujsLoIIYYxcSaWiLTqHXPblVatDjMUCz9Vud3saW1S8aR4vsb5eJ098Ukc7"><div class="choice-group" role="radiogroup"><ul class="radio-group-items"><li><input type="radio" id="collections-action-dialog-new" class="collections-new" name="collections" value="new" data-ga-category="collections_button" data-ga-action="click" data-ga-label="collections_radio_new"><label for="collections-action-dialog-new">Create a new collection</label></li><li><input type="radio" id="collections-action-dialog-existing" class="collections-existing" name="collections" value="existing" checked="true" data-ga-category="collections_button" data-ga-action="click" data-ga-label="collections_radio_existing"><label for="collections-action-dialog-existing">Add to an existing collection</label></li></ul></div><div class="controls-wrapper"><div class="action-panel-control-wrap new-collections-controls"><label for="collections-action-dialog-add-to-new" class="action-panel-label required-field-asterisk"> Name your collection: </label><input type="text" name="add-to-new-collection" id="collections-action-dialog-add-to-new" class="collections-action-add-to-new" pattern="[^"&=<>\/]*" title="The following characters are not allowed in the Name field: "&=<>/" maxlength="100" data-ga-category="collections_button" data-ga-action="create_collection" data-ga-label="non_favorties_collection"><div class="collections-new-name-too-long usa-input-error-message selection-validation-message"> Name must be less than 100 characters </div></div><div class="action-panel-control-wrap existing-collections-controls"><label for="collections-action-dialog-add-to-existing" class="action-panel-label"> Choose a collection: </label><select id="collections-action-dialog-add-to-existing" class="action-panel-selector collections-action-add-to-existing" data-ga-category="collections_button" data-ga-action="select_collection" data-ga-label="($('.collections-action-add-to-existing').val() === 'Favorites') ? 'Favorites' : 'non_favorites_collection'"></select><div class="collections-retry-load-on-error usa-input-error-message selection-validation-message"> Unable to load your collection due to an error<br><a href="#">Please try again</a></div></div></div><div class="action-panel-actions"><button class="action-panel-submit" type="submit" data-loading-label="Adding..." data-pinger-ignore data-ga-category="collections_button" data-ga-action="click" data-ga-label="add"> Add </button><button class="action-panel-cancel" aria-label="Close 'Add to Collections' panel" ref="linksrc=close_collections_panel" aria-controls="collections-action-panel" aria-expanded="false" data-ga-category="collections_button" data-ga-action="click" data-ga-label="cancel"> Cancel </button></div></form></div></div></div></div><button class="more-actions-button more-actions-dialog-trigger" title="Open dialog with more actions to take" ref="linksrc=more_actions_btn"></button><div class="display-options" 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class="journal-actions dropdown-block"><button id="full-view-journal-trigger" class="journal-actions-trigger trigger" ref="linksrc=journal_actions_btn" title="ACS nano" tabindex="0" aria-controls="full-view-journal" aria-expanded="false" aria-label="Toggle dropdown menu for journal ACS nano" data-pinger-ignore> ACS Nano </button><div id="full-view-journal" class="journal-actions-dropdown dropdown dropdown-container" hidden aria-label="Dropdown menu for journal ACS nano"><div class="title">Actions</div><div class="content"><ul class="journal-actions-links"><li><a class="search-in-pubmed-link dropdown-block-link" href="/?term=%22ACS+Nano%22%5Bjour%5D&sort=date&sort_order=desc" data-href="/?term=%22ACS+Nano%22%5Bjour%5D&sort=date&sort_order=desc" ref="linksrc=search_in_pubmed_journal_name_link&journal_abbrev=ACS Nano" data-ga-category="search" data-ga-action="journal_link" data-ga-label="ACS Nano"> Search in PubMed </a></li><li><a class="search-in-nlm-catalog-link dropdown-block-link" ref ="linksrc=search_in_nlm_catalog_link" href="https://www.ncbi.nlm.nih.gov/nlmcatalog?term=%22ACS+Nano%22%5BTitle+Abbreviation%5D" data-ga-category="search_catalog" data-ga-action="journal_link" data-ga-label="ACS Nano"> Search in NLM Catalog </a></li><li><a class="add-to-search-link dropdown-block-link" ref ="linksrc=add_to_search_link" role="button" data-search-term='"ACS Nano"[jour]' data-ga-category="search" data-ga-action="add_to_search" data-ga-label='"ACS Nano"[jour]' href="#"> Add to Search </a></li></ul></div></div></div><span class="period">. </span><span class="cit">2012 Jan 24;6(1):609-14.</span> </div> <span class="citation-doi"> doi: 10.1021/nn204012y. </span> <span class="secondary-date"> Epub 2011 Nov 28. </span> </div> <h1 class="heading-title"> Crystalline assemblies and densest packings of a family of truncated tetrahedra and the role of directional entropic forces </h1> <div class="inline-authors"> <div class="authors"> <div class="authors-list"> <span class="authors-list-item "><a class="full-name" href="/?term=Damasceno+PF&cauthor_id=22098586" ref="linksrc=author_name_link" data-ga-category="search" data-ga-action="author_link" data-ga-label="Pablo F Damasceno">Pablo F Damasceno</a><sup class="affiliation-links"><span class="author-sup-separator"> </span><a class="affiliation-link" title="Applied Physics Program, University of Michigan, Ann Arbor, Michigan 48109, USA." href="#full-view-affiliation-1" ref="linksrc=author_aff"> 1 </a></sup><span class="comma">, </span></span><span class="authors-list-item "><a class="full-name" href="/?term=Engel+M&cauthor_id=22098586" ref="linksrc=author_name_link" data-ga-category="search" data-ga-action="author_link" data-ga-label="Michael Engel">Michael Engel</a><span class="comma">, </span></span><span class="authors-list-item "><a class="full-name" href="/?term=Glotzer+SC&cauthor_id=22098586" ref="linksrc=author_name_link" data-ga-category="search" data-ga-action="author_link" data-ga-label="Sharon C Glotzer">Sharon C Glotzer</a></span> </div> </div> </div> <div class="short-article-details"> Affiliations <button class="more-details" id="toggle-authors" data-alt-text="Collapse" aria-controls="expanded-authors" aria-expanded="false" data-pinger-ignore data-fetch-url="/22098586/long-authors/" data-id-prefix=""> <span class="title"> Expand </span> </button> </div> <div class="extended-article-details" id="expanded-authors" aria-hidden="true"> <div class="expanded-authors" id="full-view-expanded-authors"> <div class="affiliations"> <h3 class="title"> Affiliation </h3> <ul class="item-list"> <li data-affiliation-id="full-view-affiliation-1" id="full-view-affiliation-1" ><sup class="key">1</sup> Applied Physics Program, University of Michigan, Ann Arbor, Michigan 48109, USA.</li> </ul> </div> </div> </div> <ul class="identifiers" id="full-view-identifiers"> <li> <span class="identifier pubmed"> <span class="id-label"> PMID: </span> <strong class="current-id" title="PubMed ID">22098586</strong> </span> </li> <li> <span class="identifier doi"> <span class="id-label"> DOI: </span> <a class="id-link" target="_blank" rel="noopener" ref="linksrc=article_id_link&article_id=10.1021/nn204012y&id_type=DOI" href="https://doi.org/10.1021/nn204012y" data-ga-category="full_text" data-ga-action="DOI" > 10.1021/nn204012y </a> </span> </li> </ul> <div class="in-clipboard-label " hidden> Item in Clipboard </div> </div> <div class="short-view" id="short-view-heading"> <h1 class="heading-title"> Crystalline assemblies and densest packings of a family of truncated tetrahedra and the role of directional entropic forces </h1> <div class="short-citation"> <span class="authors-list"> <span class="authors-list-item "><span class="full-name">Pablo F Damasceno</span><span class="citation-separator"> et al.</span></span> </span> <span class="citation-journal"> ACS Nano<span class="citation-separator">.</span> </span> <span class="date"> <time class="citation-year" datetime="2012">2012</time><span class="citation-separator">.</span> </span> </div> <div class="more-article-details-section with-display-settings"> <button class="more-article-details" id="toggle-article-details" data-alt-text="Hide details" ref="linksrc=toggle_article_details" aria-controls="full-article-details" aria-expanded="false" data-fetch-url="/22098586/long-authors/" data-id-prefix=""> <span class="title">Show details</span> </button> <div class="display-options" data-format-key="format" data-default-format-value="abstract" data-current-format-value="abstract" role="region"> <button class="trigger usa-button" title="Change format" data-ga-category="display_options" data-ga-action="display_options_dialog"> <span class="button-label">Display options</span> </button> <div class="dropdown" hidden> <div class="title"> Display options </div> <div class="content"> <div class="format-container"> <span class="option-label"> Format </span> <select name="format" 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dropdown-block-link" href="/?term=%22ACS+Nano%22%5Bjour%5D&sort=date&sort_order=desc" data-href="/?term=%22ACS+Nano%22%5Bjour%5D&sort=date&sort_order=desc" ref="linksrc=search_in_pubmed_journal_name_link&journal_abbrev=ACS Nano" data-ga-category="search" data-ga-action="journal_link" data-ga-label="ACS Nano"> Search in PubMed </a></li><li><a class="search-in-nlm-catalog-link dropdown-block-link" ref ="linksrc=search_in_nlm_catalog_link" href="https://www.ncbi.nlm.nih.gov/nlmcatalog?term=%22ACS+Nano%22%5BTitle+Abbreviation%5D" data-ga-category="search_catalog" data-ga-action="journal_link" data-ga-label="ACS Nano"> Search in NLM Catalog </a></li><li><a class="add-to-search-link dropdown-block-link" ref ="linksrc=add_to_search_link" role="button" data-search-term='"ACS Nano"[jour]' data-ga-category="search" data-ga-action="add_to_search" data-ga-label='"ACS Nano"[jour]' href="#"> Add to Search </a></li></ul></div></div></div><span class="period">. </span><span class="cit">2012 Jan 24;6(1):609-14.</span> </div> <span class="citation-doi"> doi: 10.1021/nn204012y. </span> <span class="secondary-date"> Epub 2011 Nov 28. </span> </div> <div class="expanded-authors" id="short-view-expanded-authors"> <div class="authors"> <h3 class="title"> Authors </h3> <div class="authors-list"> <span class="authors-list-item "><a class="full-name" href="/?term=Damasceno+PF&cauthor_id=22098586" ref="linksrc=author_name_link" data-ga-category="search" data-ga-action="author_link" data-ga-label="Pablo F Damasceno">Pablo F Damasceno</a><sup class="affiliation-links"><span class="author-sup-separator"> </span><a class="affiliation-link" title="Applied Physics Program, University of Michigan, Ann Arbor, Michigan 48109, USA." href="#short-view-affiliation-1" ref="linksrc=author_aff"> 1 </a></sup><span class="comma">, </span></span><span class="authors-list-item "><a class="full-name" href="/?term=Engel+M&cauthor_id=22098586" ref="linksrc=author_name_link" data-ga-category="search" data-ga-action="author_link" data-ga-label="Michael Engel">Michael Engel</a><span class="comma">, </span></span><span class="authors-list-item "><a class="full-name" href="/?term=Glotzer+SC&cauthor_id=22098586" ref="linksrc=author_name_link" data-ga-category="search" data-ga-action="author_link" data-ga-label="Sharon C Glotzer">Sharon C Glotzer</a></span> </div> </div> <div class="affiliations"> <h3 class="title"> Affiliation </h3> <ul class="item-list"> <li data-affiliation-id="short-view-affiliation-1" id="short-view-affiliation-1" ><sup class="key">1</sup> Applied Physics Program, University of Michigan, Ann Arbor, Michigan 48109, USA.</li> </ul> </div> </div> <ul class="identifiers" id="short-view-identifiers"> <li> <span class="identifier pubmed"> <span class="id-label"> PMID: </span> <strong class="current-id" title="PubMed ID">22098586</strong> </span> </li> <li> <span class="identifier doi"> <span class="id-label"> DOI: </span> <a class="id-link" target="_blank" rel="noopener" ref="linksrc=article_id_link&article_id=10.1021/nn204012y&id_type=DOI" href="https://doi.org/10.1021/nn204012y" data-ga-category="full_text" data-ga-action="DOI" > 10.1021/nn204012y </a> </span> </li> </ul> <div class="in-clipboard-label " hidden> Item in Clipboard </div> </div> </div> </header> <div class="actions-buttons inline"><div class="inner-wrap"><button class="full-text-links-button full-text-links-dialog-trigger" title="Open dialog with full text links" ref="linksrc=full_text_links"> Full text links </button><button class="citation-button citation-dialog-trigger" aria-label="Open dialog with citation text in different styles" data-ga-category="save_share" data-ga-action="cite" data-ga-label="open" data-all-citations-url="/22098586/citations/" data-citation-style="nlm" data-pubmed-format-link="/22098586/export/"><span class="button-label">Cite</span></button><button class="more-actions-button more-actions-dialog-trigger" title="Open dialog with more actions to take" ref="linksrc=more_actions_btn"></button><div class="display-options" data-format-key="format" data-default-format-value="abstract" data-current-format-value="abstract" role="region"><button class="trigger usa-button" title="Change format" data-ga-category="display_options" data-ga-action="display_options_dialog"><span class="button-label">Display options</span></button><div class="dropdown" hidden><div class="title"> Display options </div><div class="content"><div class="format-container"><span class="option-label"> Format </span><select name="format" data-initial-value="abstract" aria-label="Display format" id="inline-actions-display-format"><option value="abstract">Abstract</option><option value="pubmed">PubMed</option><option value="pmid">PMID</option></select></div></div></div></div></div></div> <div class="abstract" id="abstract"> <h2 class="title"> Abstract </h2> <div class="abstract-content selected" id="eng-abstract"> <p> Polyhedra and their arrangements have intrigued humankind since the ancient Greeks and are today important motifs in condensed matter, with application to many classes of liquids and solids. Yet, little is known about the thermodynamically stable phases of polyhedrally shaped building blocks, such as faceted nanoparticles and colloids. Although hard particles are known to organize due to entropy alone, and some unusual phases are reported in the literature, the role of entropic forces in connection with polyhedral shape is not well understood. Here, we study thermodynamic self-assembly of a family of truncated tetrahedra and report several atomic crystal isostructures, including diamond, β-tin, and high-pressure lithium, as the polyhedron shape varies from tetrahedral to octahedral. We compare our findings with the densest packings of the truncated tetrahedron family obtained by numerical compression and report a new space-filling polyhedron, which has been overlooked in previous searches. Interestingly, the self-assembled structures differ from the densest packings. We show that the self-assembled crystal structures can be understood as a tendency for polyhedra to maximize face-to-face alignment, which can be generalized as directional entropic forces. </p> </div> </div> <p class="copyright" id="copyright"> © 2011 American Chemical Society </p> <p class="disclaimer" id="disclaimer"> <a href="/disclaimer/" target="_blank" data-ga-category="literature_resources" data-ga-action="disclaimer_link" data-ga-label="under_abstract">PubMed Disclaimer</a> </p> <div class="similar-articles" id="similar"> <h2 class="title"> Similar articles </h2> <ul class="articles-list" id="similar-articles-list"> <li class="full-docsum"> <div class="docsum-content" style="display:inline;"> <a class="docsum-title" href="/19905270/" ref="article_id=19905270&linksrc=similar_articles_link&ordinalpos=1" data-ga-category="similar_article" data-ga-action="19905270" data-ga-label=""> Dense packings of polyhedra: Platonic and Archimedean solids. </a> <div class="docsum-citation full-citation"> <span class="docsum-authors full-authors">Torquato S, Jiao Y.</span> <span class="docsum-authors short-authors">Torquato S, et al.</span> <span class="docsum-journal-citation full-journal-citation">Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Oct;80(4 Pt 1):041104. doi: 10.1103/PhysRevE.80.041104. 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Crystalline assemblies and densest packings of a family of truncated tetrahedra and the role of directional entropic forces - PubMed